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Alcohol and tobacco use are leading modifiable risk factors for non-communicable diseases (NCDs) worldwide. In sub-Saharan Africa, including Uganda, these behaviors are increasingly common but often analyzed separately, limiting understanding of their shared determinants. This study used nationally representative data from the 2014 Uganda WHO STEPS survey to examine individual and joint predictors of current alcohol and tobacco use among adults aged 18-69. Using separate and joint logistic regression models, we assessed associations with demographic, socioeconomic, and health-related factors, applying a shared random effect in the joint model to account for within-individual correlation. The joint model provided better fit (AIC = 6850.13) than the combined separate models (AIC = 6890.73), suggesting a shared latent structure influences both outcomes. Female sex and higher educational attainment were consistently associated with lower odds of substance use, while older age and being separated, divorced, or widowed were linked to higher odds. Smoking-specific interactions showed stronger effects in older and underweight individuals and regional differences were more pronounced for smoking than alcohol. These findings highlight the presence of shared and distinct determinants underlying alcohol and tobacco use in Uganda. While the results suggest potential value in considering these behaviors jointly, further research is needed to evaluate whether integrated intervention strategies are effective in reducing co-occurring substance use.